Answer to Question #104650 in Macroeconomics for Mitchell

Question

Answer the following questions using the aggregate expenditures model of the economy described below C = 80 + .6Ya, T = 40 + .2Y, la-28, Ga-64, Xa-76, and M-18Y Required (a) What is the saving function? What is the marginal propensity to save? (b) What is the aggregate expenditure function? What is autonomous expenditure? What is the marginal propensity to withdraw? (e) What is the cquilibrium level of real GDP? (d) What is the size of the multiplier? e) Suppose the full employment level of real GDP is $340. Does a recessionary gap or an inflationary gap exist? How can the government eliminate the gap by altering government expenditures?

Answer 1

a) Savings Function -mirror Consumption Functions

S(у) = S0 + MPS*Yv или -С0 + MPS*Yv=-80 + .6Yd

Marginal propensity to save (МРS) - the share of any growth in income that goes to savings:

MPS = (∆S / ∆Y) * 100%.

b) Total costs in the economy represent the total amount of expenses borne by consumers, business and the state for the purchase of products produced in society. In this regard, and subject to the reservations made, the total costs will be:

C=C+I+G+(X-M)=80+ .6Yd+28+64+(76- .18Y)=248+.6Yd-.18Y

Autonomous expenses are expenses that are independent of the dynamics of national income

A= I+С=28+80+ .6Yd=108+ .6Yd

The marginal propensity to withdraw(MPW) is the effect of a change in income on withdrawals. It is defined as the change in total withdrawals as a proportion of the change in income. MPW =change in total withdrawals/change in income

c)Equilibrium is considered to be such a volume of production that ensures equality of total expenditures in the economy and the volume of products produced in society. Equilibrium output — equilibrium GDP — such a volume of production that provides total expenditures sufficient for the implementation of this volume of production, i.e., with an equilibrium GDP, the total cost of goods produced is equal to the cost of goods sold (purchased): equilibrium GDP = AE, or equilibrium GDP = C+ I. This is the condition under which all manufactured products are sold out, i.e. there are no surpluses or shortages on the national market.

equilibrium GDP = C+ I=28+80+ .6Yd=108+ .6Yd

d)The multiplier is equal to the inverse of the marginal propensity to save (and the inverse of any numeric value is the quotient obtained from dividing a unit by a given number), so K = 1/MPS.

 The multiplier effect also depends on the marginal propensity to consume (MPC). Since consumption and savings in total are always equal to one (MPC + MPS = 1), then MPS = 1 - MPC. Accordingly, the multiplier formula can have the following form: K= 1/(1-Mrs).

e) In this case, the recession gap. In order to overcome the recession gap and ensure full employment of resources, the state needs to stimulate aggregate demand through public investment in the economy